Preheat the oven to 375 degrees F. Line a baking sheet with parchment.
Melt the butter in a large saucepan over medium-high heat. When it begins to foam, add the mushrooms, leeks and 1/4 teaspoon salt, and cook, stirring, until well browned, 2 to 3 minutes. Add the curry powder, and cook for 30 seconds, stirring. Add the cauliflower, tomatoes, 1/2 cup water and 1/2 teaspoon salt, and stir, scraping up the spice paste from the bottom of the pan. Bring to a simmer, cover, reduce the heat to low and cook until the sauce has thickened and the cauliflower is tender, about 4 minutes. Remove the lid and, if necessary, continue to cook until the sauce is a thick, almost paste-like consistency and coats the vegetables, about 1 minute more. Transfer the filling to a medium bowl, and let cool completely. Stir in the peas.
Unfold the puff pastry onto a lightly floured surface, and roll it out into a 12-inch square.
Quarter the dough to make 4 equal squares. Put a quarter of the filling in the center of each square. Sprinkle 1/4 cup of the Cheddar on the top of each mound. Brush the edges of each square with the beaten egg, then fold 1 corner on top of the opposite corner, making a triangle. Transfer to the prepared baking sheet. Press along the edges with the back of a fork to create a pattern and seal the turnover. Brush each turnover with egg, and make 3 small slits on the top. Sprinkle each with 2 tablespoons of the remaining Cheddar.
Bake until the turnovers are golden brown and bubbly, 30 to 35 minutes. Serve hot with mango chutney if using.